00:01
Question 58 tells you that g of x equals 4 minus sine of 2x plus pi over 2 is related to either parent function sinex or cosine x.
00:10
And in part a, they want you to describe the series of transformations to get f to g.
00:17
And our parent function here would be sine of x because g is a sign function.
00:20
And you want to use the formula y equals d plus a sign of bx minus c.
00:26
Starting off for sinex, you know that our amplitude absolute value of a is just one period.
00:31
2 pi over b is 2 pi, and we are ranging from 0 to 2 pi on the x -axis.
00:44
For g of x, our amplitude here is just going to be absolute value of negative 1, which is just 1.
00:59
Our period 2 pi over b our b here is 2 so our period is just pi our endpoints using the formula c over b less than equal to x less than equal to c over b equals 2 pi over b b in this case is negative pi over 2 and therefore we have the end points negative pi over 4 less than equal to x less than equal to 3 pi over 4 d here here in this case is also equal to 4, which means we're shifting up by 4 units.
01:43
You also should recall in terms of this negative sign in front of sine x, y equals negative f of x is a reflection over the x -axis of y equals f of x.
02:01
So our graph here will be flipped.
02:04
And the final conclusions we can make is g is f with half the period.
02:18
A reflection over the x -axis, a horizontal shift to the left of pi over four, and a vertical shift of four units up.
02:50
That's part a.
02:51
For part b, they want you to then graph this function.
02:56
So we want to find our key points...